I’m particularly interested in how emulators deal with the mismatch between the FPU of the target hardware versus the host.

It’s a fascinating and frustrating topic when you’re trying to emulate floating point in a specific way using hardware that doesn’t exactly do what you need. But almost. For example, maybe your host rounds differently or uses different status flags so the challenge is to find as many cases as possible where you can still exploit your host FPU without generating incorrect results.